With the increase of huge amounts of data in volume, velocity, and variety, the need for capacity of Redundant Arrays of Inexpensive Disks (RAID) storage systems is dramatically growing. However, the probability of disk failures in RAID storage systems is sharply high with the increase of program/erase cycles, read cycles, and retention time. Furthermore, they are faced with more challenges in fault tolerance, storage efficiency, computational complexity, and expandability. This article presents a novel data layout scheme for RAID storage System using Random Binary Extensive Code (RBEC), which are designed to ensure random expandability, high reliability, and availability of data in RAID storage systems. RBEC is a family of systematic code, in which the generator matrix consists of two submatrices with entries over GF(2), an identity matrix on the top, and another submatrix on the bottom. Compared with the existed approaches, the attractive advantages of our schemes include 1) they are completely implemented based on only simple eXclusive OR (XOR) operations and have systematic code property, 2) they can provide arbitrary fault tolerance, 3) their storage efficiency is quasi-optimal, and 4) data and parity disks of RAID storage systems can be randomly expanded according to practical requirements. Thus, our scheme is particularly suitable for RAID storage systems that need higher reliability, availability, and expandability.